The general expression derived previously (A.P. Kouzov, J.V. Buldyreva, A.V. Sokolov, J. Chem. Phys. 149, 044305 (2018)) for the frequency-dependent rotational relaxation matrix describing collisions of linear molecules is put into an energy-corrected-sudden (ECS) form convenient for spectra modeling. The translational interaction spectral functions characterizing the intracollisional dynamics and determining the relaxation matrix elements are factorized into a frequency-dependent and an anisotropy ranks-dependent parts. The particular case of isotropic Raman Q-branch enables to establish connections of these parts with the adiabaticity factor accounting for the molecular rotation during the collision and the bimolecular relaxation rates, respectively. Analyses of these rates allow suggesting their realistic exponential-polynomial model representations with a few adjustable parameters determined from fits on experimentally available (Formula presented.) line widths. Thanks to the universal character of the non-Markovian approach, the same parameters enable realistic computations of (Formula presented.) anisotropic Raman spectra up to very far spectral wings and without any additional parameter with respect to the Markovian ECS.